All-Norms and All-L_p-Norms Approximation Algorithms

Daniel Golovin, Anupam Gupta, Amit Kumar & Kanat Tangwongsan
In many optimization problems, a solution can be viewed as ascribing a ``cost\'\' to each client, and the goal is to optimize some aggregation of the per-client costs. We often optimize some $L_p$-norm (or some other symmetric convex function or norm) of the vector of costs---though different applications may suggest different norms to use. Ideally, we could obtain a solution that optimizes several norms simultaneously. In this paper, we examine approximation algorithms that simultaneously perform...